A hydraulic multi-circuit brake system of this type is already known (German Published, Non-Examined Patent Application DE-OS 37 41 310; U.S. Pat. No. 4,861,116), where the first valve assembly of the wheel brake assigned to the non-powered vehicle wheel consists of two 2/2-way valves, of which the so-called inlet valve is located in the brake line, while the so-called outlet valve has a third connection of the first valve assembly and is located in an outflow line which originates at the brake line between the inlet valve and the wheel brake and leads to the input side of the pump. In the case of traction control operation, the two directional control valves of the first valve assembly are placed in the open position and the second valve assembly in the brake line of the powered vehicle wheel is in the blocking position, so that the pump can aspirate pressure medium from a pressure medium reservoir via the main brake cylinder, supply it to the brake line of the powered vehicle wheel and build up brake pressure in the assigned wheel brake. In this case, because of the outlet valve assuming its open position, generation of harmful underpressure in the wheel brake cylinder of the non-powered wheel at the start of the pressure means that supply is not completely impossible. Furthermore, when the driver triggers braking in the case of traction control operation, brake pressure cannot immediately build up in the wheel brake cylinders, since the brake line of the wheel brake assigned to the powered wheel is blocked until the switching of the second valve assembly, and the pressure medium supplied to the brake line of the wheel brake assigned to the non-powered vehicle wheel can flow off towards the pump until the outlet valve is closed.